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Spring 2018, CMPSC/MATH 451Homework Assignment #1Due 11.59 pm, February 8 on CanvasLast updated February 7 with hints and corrections (problem 3 pseudocode).1Let x be a given nonzero oating-point number in a normalized system, and let y be an adjacentoating-point number, also non-zero. What is the minimum possible spacing between x and y?What is the maximum possible spacing between x and y? How are these results a ected by therounding rule used? Hint: Note that x and y are two adjacent positive numbers. For instance, ina normalized oating-point system with base 10, precision 4, L = 3, and U = 10, 2.151 and 2.152are adjacent numbers. You need to give a general expression for the minimum/maximum possiblespacing in terms of , p, L, and U.(6 points)2Suppose a machine with a oating-point system ( ;p;L;U) = (10;6; 30;20) is used to calculatethe roots of the quadratic equation ax2 +bx+c = 0, where a, b, and c are given, real coe cients.For each of the following cases, state the numerical di culties that arise if one uses the standardformula for computing the roots. Explain how one can overcome these di culties (when possible):a = 105;b = 1012;c = 106a = 10;b = 104;c = 1a = 2;b = 8;c = 8:00001(9 points)3Prepare a MATLAB/Octave script. that sums n random, single-precision oating-point numbers xi,uniformly distributed in the interval [0;1]. Sum the numbers in each of the following ways (usingsingle-precision variables unless speci cally indicated otherwise):(a) Sum the numbers in the order in which they were generated, using a double-precision variableto accumulate the sum. Use a loop to do the summation and not the builtin function.(b) Sum the numbers in the order in which they were generated, this time using a single-precisionaccumulator. Use a loop to do the summation and not the builtin function.(c) Use the following compensated summation algorithm, again using only single precision, to sumthe numbers in the order in which they were generated:s = 0c = 0for i = 1 to n do1y = xi ct = s+yc = (t s) ys = tend for(d) Sum the numbers in order of increasing magnitude (using the builtin sort function). Use aloop to do the summation (after sorting the numbers) and not the builtin function.(e) Sum the numbers in decreasing magnitude (reversing the order obtained in the previous part).Use a loop to do the summation and not the builtin function.Once you check for correctness, extend the previous program to answer the following:(i) Experiment with di erent values of n and chart your results. Note that you may need to usefairly large values of n to see substantial di erences.(ii) How do the methods rank in terms of accuracy, and why? You can use the result of thebuiltin function sum as the true value. Do not use the builtin function for(iii) How do the methods compare in cost? Time the routines for a large n and provide a com-parison.(iv) Brie y explain how/why the compensated summation algorithm works.(25 points)13 points for code + 12 points for responses to the four questions 4Chapter 3, exercise 1 (pages 58 and 59).(10 points)本团队核心人员组成主要包括BAT一线工程师，精通德英语！我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域：window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业，所以值得信赖。如有需要，请加QQ：99515681 或邮箱：[email protected] 微信：codehelp QQ：99515681 或邮箱：[email protected] 微信：codehelp